[47] Strain wave gearing design system

Transcription

1 [47] Strain wave gearing design system Fig.47.3 Property and basic rack(cup type) Fig.47.1 Strain wave gearing design system 47.1 Overview Strain wave gearing design system is a software that generates wave gear tooth profile, based on basic rack or tool (hob). Meshing of the generated tooth profile and rendering can be displayed, and also 2D-DXF file output can be generated. Overall display is shown in Table Software configuration Strain wave gearing design system configuration is shown in Table Table 47.1 Software Configuration No. Item Figure Basic rack Tool(HOB) Type of Ring Tool dimension Gear dimension Tooth profile Tooth modification DTooth profile Tooth rendering FEM-Analysis Hertzian stress Output (Tooth profile) Design-data management Basic Rack(Property) Basic rack (cup type) is shown in Figure As basic rack can be chosen between full depth tooth, low tooth and special tooth, initialize is used to set up special tooth with α=25,h ac =0.8, h fc =1.05, r c = After basic rack is specified, actual basic rack can be displayed as shown by Figure 47.3, by clicking. (Hob-based tooth profile is shown in Figure 47.12) 47.4 Dimension Dimension display is shown in Figure 47.4 by using the example with m n =0.3, z FS =100,z CS =102.Although the addendum modification coefficient is shown as x n =0.2, it can be set to any value. Also, tip R can be defined all the way to the addendum pointed limit.in basic rack root R, the value specified in Figure 47.2 is taken as the standard value, but it can be defined all the way to the established limit of basic rack profile. The input range is shown below. Module : 0<m n <10 Number of teeth : 10<z FS 1000,z FS +2<z CS 1000 Profile shift : -2<x n <+3 Face width : 0<b <1000 Fig.47.4 Gear dimensions 47.5 Tooth profile calculation The tooth profile calculation setup display is shown in Figure Flex spline thickness, device outer diameter and number of divisions for tooth profile calculation set-up can be specified. After setting the values, click to proceed to tooth profile calculation. Fig.47.5 Tooth Profile Set-up Fig.47.2 Basic rack(cup type) 47.6 Tooth profile modification Generated flex spline tooth profile can be modified as shown in Figure Tooth profile can be specified either by line of action or diameter, while the magnification of the tooth profile modification can be selected from 50, 100, 200, 300, 400, 500,

2 Fig.47.6 Tooth Profile Modification The tooth profile modification can be applied by track-bar (shown at the center of Figure 47.7) and table-entry on the right hand side of the screen. In Figure 47.7, tooth profile is shown with 9 divisions, but it can be specified up to 50 divisions. Also, connection of the tooth profile can be spline (as shown by this example) or straight line connection. Moreover, numerical value can be entered into the template figure as shown in Figure (a) Section[A] (b) Section [B] (c) Section [C] (d) Section [D] Fig Enlarged figure at each section Fig.47.7 Profile modification setup Fig Distance measurement 47.8 Rendering Tooth profile can be displayed as shown in Figure This rendering can be enlarged, reduced and rotated by using. Fig.47.8 Profile modification setup (Template) 47.7 Tooth Profile Figure (2D) Generated tooth profile can be displayed as shown in Figure Enlarged sections [A] to [D] are shown in Figure Also, distance can be measured as shown in Figure Moreover, rotation-related tooth profile meshing can be checked by rotation in right hand corner of Figure [E] Fig Rendering and supplemental form [A] [B] [C] [D] Fig.47.9 Tooth Profile & Supplemental Feature Fig Rendering enlargement[e] 47.9 FEM Analysis (2D) When load is applied to teeth, root stress in the teeth can be calculated. FEM analysis setup display is shown in Figure 47.14, but in FEM analysis, material is symbols only, as it is based on longitudinal elastic modulus and Poisson's ratio. Vertical division number and horizontal 168

3 division number can be specified arbitrarily. The position of the load (2 in the example: the second node from the tooth tip), less than 2 in the vertical division number can be specified. For the load applied in this case, please set the value per designer s intension Tooth contact stress The calculation of Hertzian stress acting on tooth surface is shown in Figure The purpose of this feature is to compare the Hertzian stress due to tooth profile differences, so the load acting on one tooth should be designer s intended value. Fig FEM analysis setup FEM analysis results are shown in Figure to The analysis items are, and flex spline max main stress is found to be σ 1max =24.0MPa as shown in Figure Also, displacement figure is shown in Figure while stress summary (selective results only) is shown in Figure Fig Hertzian Stress Tooth profile output The resulting F/S (perfect circle), F/S (ellipse) and C/S tooth profile output can be generated. F/S tooth profile output display is shown in Figure while CAD drawing sample is shown in Figure Fig Flex Spline, σ 1max =14.4MPa Fig F/S Tooth profile output setup (a) F/S(perfect circle) F/S(Ellipse) (c) C/S Fig CAD Drawing sample Fig Circular spline,σ 1max =13.4MPa Tooth profile made by hob Hob dimensions When hob blade profile is known, the hob profile can be defined by selecting cup in reducer type property in Figure Fig Flex Spline displacement, δmax=0.08μm Fig Property, Cup type (Special tool) Fig Stress Summary (selective results) Hob dimension input sample is shown in Figure In this sample, pitch= is used to achieve module 0.3, but any value can be specified. After input entry, true hob profile can be displayed by clicking profile. The hob profile is based on gear front surface. 169

4 Figure Also, there is 22μm of gap between tooth tips in [F], and there is 2.6μm of gap between teeth in [G]. The clearance is 0.07mm as shown in Figure 47.40, and F/S tip area is found to be arc-shape of 0.359mm as calculated in Figure When gear is specified as over-pin, tooth profile and pin are contacting as shown in Figure 47.42, and F/S contact diameter is found to be d c =33.01mm. Fig Hob dimensions [E] [G] [F] Fig Tooth profile Fig Hob profile Gear Dimensions In Figure 47.4, module was entered, but module, pressure angle and root diameter cannot be entered in Figure because pitch is already entered in Figure (background is grayed out). (a) [E] section (b) [F] section Fig Enlarged tooth profile Fig Gear dimensions Fig Enlarged tooth profile [G] section, distance measurement Tooth profile After gear dimensions are specified, tooth profile calculation is performed based on rim thickness and outer diameter as shown in Figure Fig Distance measurement Fig Arc measurement Fig Rim thickness and outer diameter After tooth profile calculation is completed, transverse tooth profile can be displayed as shown in Figure However, tooth profile modification cannot be performed when it is based on hob. Since C/S tooth profile is generated to mesh with F/S tooth profile, both gears are contacting without any gaps as shown in the enlarged view of [E] in (a) F/S & Pin (b) C/S & Pin Fig Pin positions 170

5 After tooth profile is generated, tooth profile rendering can be displayed as shown in Figure This figure can be rotated just like 2D tooth profile, while changing observation angle in the supplemental form CAD drawing sample Drawing samples are shown in Fig to Fig F/S(circle) F/S(ellipse) Fig CAD drawing sample, Fig Rendering & supplemental form FEM analysis & Hertzian stress Analysis results are shown in Fig to Fig Fig CAD drawing sample, C/S Design data management Design data can be managed as shown in Figure 47.51, while it can be also imported and exported as shown in Figure Fig FEM analysis setup Fig Design data management Fig Flex spline, σ 1max =11.5MPa Fig File management Fig Circular spline, σ 1max =472MPa Fig Ring type, m=0.15, z 1 =z 3 =200, z 2 =204 Fig Hertzian stress 日本語版カタログは別途お申しつけください. 171